AbstractAnswer Set Programming Research Articles

IASCAR: Incremental Answer Set Counting by Anytime Refinement

Abstract Answer set programming (ASP) is a popular declarative programming paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If one counts under assumptions on literals, one obtains a tool to comprehend parts of the solution space, so-called answer set navigation. However, navigating through parts of the solution space requires counting many times, which is expensive in theory. Knowledge compilation compiles instances into representations on which counting works in polynomial time. However, these techniques exist only for conjunctive normal form (CNF) formulas, and compiling ASP programs into CNF formulas can introduce an exponential overhead. This paper introduces a technique to iteratively count answer sets under assumptions on knowledge compilations of CNFs that encode supported models. Our anytime technique uses the inclusion–exclusion principle to improve bounds by over- and undercounting systematically. In a preliminary empirical analysis, we demonstrate promising results. After compiling the input (offline phase), our approach quickly (re)counts.

CNL2ASP: Converting Controlled Natural Language Sentences into ASP

Abstract Answer set programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may find it more advantageous to employ a higher-level language that closely resembles natural language when specifying ASP programs. In this paper, we propose a novel tool, called CNL2ASP, for translating English sentences expressed in a controlled natural language (CNL) form into ASP. In particular, we first provide a definition of the type of sentences allowed by our CNL and their translation as ASP rules and then exemplify the usage of the CNL for the specification of both synthetic and real-world combinatorial problems. Finally, we report the results of an experimental analysis conducted on the real-world problems to compare the performance of automatically generated encodings with the ones written by ASP practitioners, showing that our tool can obtain satisfactory performance on these benchmarks.

An Efficient Solver for ASP(Q)

AbstractAnswer Set Programming with Quantifiers ASP(Q) extends Answer Set Programming (ASP) to allow for declarative and modular modeling of problems from the entire polynomial hierarchy. The first implementation of ASP(Q), called QASP, was based on a translation to Quantified Boolean Formulae (QBF) with the aim of exploiting the well-developed and mature QBF-solving technology. However, the implementation of the QBF encoding employed in qasp is very general and might produce formulas that are hard to evaluate for existing QBF solvers because of the large number of symbols and subclauses. In this paper, we present a new implementation that builds on the ideas of QASP and features both a more efficient encoding procedure and new optimized encodings of ASP(Q) programs in QBF. The new encodings produce smaller formulas (in terms of the number of quantifiers, variables, and clauses) and result in a more efficient evaluation process. An algorithm selection strategy automatically combines several QBF-solving back-ends to further increase performance. An experimental analysis, conducted on known benchmarks, shows that the new system outperforms QASP.

System Predictor: Grounding Size Estimator for Logic Programs under Answer Set Semantics

AbstractAnswer set programming is a declarative logic programming paradigm geared towards solving difficult combinatorial search problems. While different logic programs can encode the same problem, their performance may vary significantly. It is not always easy to identify which version of the program performs the best. We present the system predictor (and its algorithmic backend) for estimating the grounding size of programs, a metric that can influence a performance of a system processing a program. We evaluate the impact of predictor when used as a guide for rewritings produced by the answer set programming rewriting tools projector and lpopt. The results demonstrate potential to this approach.

IMSD: Interactive Methods for Finding Similar or Diverse Answer Sets

Answer set programming (ASP) is a modeling language in knowledge representation, rooted in Logic Programming and Nonmonotonic Reasoning, which has been gaining increasing attention during the last years. In recent years, many of the researchers developed integrated development environments (IDE) for ASP programs including editors and debuggers. Other researchers focused on analyzing the answer sets, they introduced offline and online methods to find specific solutions of a given problem in answer set programming in different approaches such as phylogeny reconstruction. However, with an enormous number of answer sets could be available, the user is not interested in all of them. Thus, a navigation of the search space could be a solution to help the user to access the specific answer sets. To this end, we aim at finding similar/diverse solutions of the answer sets with a new method. The intuition behind this navigation is to make the search faster than other methods and explore information that is related to the user’s query. Afterward, we implement a tool performing the above approach in order to simplify the search task and show the applicability and effectiveness of our method. We conclude by testing the performance of the proposed tool into a real-world example of ASP programs.

IMSD: Interactive Methods for Finding Similar or Diverse Answer Sets

Answer set programming (ASP) is a modeling language in knowledge representation, rooted in Logic Programming and Nonmonotonic Reasoning, which has been gaining increasing attention during the last years. In recent years, many of the researchers developed integrated development environments (IDE) for ASP programs including editors and debuggers. Other researchers focused on analyzing the answer sets, they introduced offline and online methods to find specific solutions of a given problem in answer set programming in different approaches such as phylogeny reconstruction. However, with an enormous number of answer sets could be available, the user is not interested in all of them. Thus, a navigation of the search space could be a solution to help the user to access the specific answer sets. To this end, we aim at finding similar/diverse solutions of the answer sets with a new method. The intuition behind this navigation is to make the search faster than other methods and explore information that is related to the user’s query. Afterward, we implement a tool performing the above approach in order to simplify the search task and show the applicability and effectiveness of our method. We conclude by testing the performance of the proposed tool into a real-world example of ASP programs.

Optimum stable model search: algorithms and implementation

Abstract Answer Set Programming (ASP) is a well-known declarative problem solving paradigm developed in the field of nonmonotonic reasoning and logic programming. The usual target of ASP is the solution of combinatorial search problems, nonetheless the language of ASP was extended with weak constraints for concise modelling of optimization problems. In the case of ASP programs with weak constraints, the main computational task of an ASP solver is optimum stable model search . In this article, we present and compare several algorithms for optimum stable model search. We consider solutions traditionally adopted by ASP solvers, and we introduce new solving strategies obtained by porting to the ASP setting some algorithms that were introduced for Maximum Satisfiability solving. The article also reports on the implementation of these algorithms in the ASP solver wasp . An empirical analysis highlights pros and cons of different strategies for computing optimum stable models.

Efficient recursive aggregate evaluation in logic programming

Answer Set Programming (ASP) is a powerful formalism for knowledge representation and common sense reasoning, particularly suitable for representing incomplete knowledge and nonmonotonic reasoning. ASP is used in Artificial Intelligence applications such as diagnosis and planning. Aggregate functions are an important extension to ASP that allow the representation of concepts involving sets of data in a natural way. We have analyzed the properties of recursive aggregates, identified rich classes of programs with a unique answer set, and defined a new notion of unfounded set that we used in answer set computations. Experimental results on the implemented prototype, obtained by extending DLV, show a significant performance improvement of our enhanced approach over existing techniques. In this paper we summarize some of our results, which are fully described in the thesis of the same title.

New method for building ASP knowledge base from knowledge in classical logic

Answer Set Programming (ASP) is now a mainstream tool for the representation of non-monotonic knowledge. In order to make use of the existing knowledge in classic logic in the process of using ASP for problem solving, a method was proposed for translating knowledge in classic logic formulas to an ASP program or ASP knowledge base so that the models of the formulas and the answer sets of the ASP program were in one-to-one cor-respondence. Some examples were presented to illustrate the effectiveness of the method. Two classes of knowledge were distinguished in this paper, i.e. constraint knowledge that requires a formula to be satisfactory and definition knowledge that defines a predicate. In practice, the method provides a way of building non-monotonic ASP knowledge bases from the existing knowledge bases that use predicate logic as representation language.